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2053Lecture8 - Linear Momentum& Conservation...

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Unformatted text preview: Linear Momentum & Conservation Conservation Topics of Discussion Topics Linear Momentum Reformulation of Newton’s Second Law Conservation of Linear Momentum Types of Collisions Impulse & the Impulse-Momentum Impulse Theorem Theorem Linear Momentum Linear The linear momentum p, iin the SI units n The kgm/s, of an object with mass m moving at kgm/s of the velocity v is defined by p = mv . Newton’s Second Law and Momentum Momentum (Newton’s Second Law) The time rate The change of an object’s momentum is equal to the average force F acting on the object of mass m, and is given by ∆p F= ∆t . Conservation of Linear Momentum Conservation When no external forces are acting on a system When consisting of colliding objects, the total initial momentum is equal to the total final momentum of the system. of Let mk be the mass of the k-the particle, vki be its Let initial speed and vkf be its final speed, then the principle of linear momentum conservation for a two particle system is given by two m١v١i + m٢v٢i = m١v١ f + m٢v٢ f . Elastic Collisions Elastic Elastic collisions occur when the Elastic conservation of linear momentum and energy hold simultaneously. energy m١v١i + m٢v٢i = m١v١ f + m٢v٢ f Ebefore = Eafter Inelastic Collisions Inelastic Inelastic collisions occur when only the Inelastic occur conservation of linear momentum holds. conservation m١v١i + m٢v٢i = m١v١ f + m٢v٢ f Completely Inelastic Collisions Completely When two objects in a system of objects When stick together, they experience a completely inelastic collision, and the completely and principle of linear momentum conservation states states m١v١i + m٢v٢i = ( m١ + m٢ ) v f Remember that the conservation of energy is invalid for completely inelastic collisions. is Impulse The force F which acts over a time interval ∆t is called the impulse J delivered to a impulse system of particles, and is given by system J = F∆ t. Impulse-Linear Momentum Theorem Theorem A force acting over a time interval ∆t which force changes the speed of the body from vi to vf is equal to the change in momentum of a particle of mass m, that is that F∆ t = mv f − mvi . ...
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